The nonlinear problem of steady flow of an incompressible stratified fluid of finite depth over an obstacle is investigated by using algorithm which solves both obstacle height and flow fields simultaneously instead of solving the flow fields, given the obstacle height. We also find, for a given upstream condition, a maximum obstacle height over which steady flows are possible, not allowing discontinuities or closed streamlines. This maximum height is a functional of the upstream density stratification and the velocity shear. We calculate this functional dependence for a number of specific upstream conditions. It is also shown that the number of layers required in the model to represent a flow field increases as the Froude number decreases or as the vertical wave number increases. The hydrostatic and finite depth assumptions are essential in our method.